The Case Against JIVE
|
|
- Maximillian Gallagher
- 5 years ago
- Views:
Transcription
1 The Case Against JIVE Related literature, Two comments and One reply PhD. student Freddy Rojas Cama Econometrics Theory II Rutgers University November 14th, 2011
2 Literature 1 Literature 2 Key de nitions 3 The case against JIVE 4 The bias of 2SLS 5 Estimators UJIVE 1 UJIVE 2 JLS or JIVE LIML 6 Experiments 7 Results 8 Conclusions 9 Two comments and One reply 11 Estimation by using STATA 12 References 13 Appendix
3 Literature Instrumental variables performance with weak instruments Davidson and McKinnon (2004). The case Against JIVE. Journal of Applied Econometrics 21: Blomquist and Dahlberg (1999). Small sample properties of LIML and Jaccknife IV estimators: Experiments with Weak Instruments. Journal of Applied Econometrics 14: Angrist, J., W. Imbens and A. Krueger (1999). Jaccknife Instrumental Variables Estimation. Journal of Applied Econometrics 14:
4 Key de nitions Key de nitions Jackknife Instrumental Variables Estimation (JIVE). Unbiased Jackknife Instrumental Variables Estimation (UJIVE). Limited Information maximum likelihood (LIML) Two Stage Linear Squares (2SLS) Finite-small sample properties Monte Carlo simulations.
5 The case against JIVE JIVE performs very badly when the instruments are weak. Davidson and McKinnon (2004) [DM] perform montecarlo experiments to compare the performance of "jackknife instrumental variables estimator" with the 2SLS and LIML estimators. They nd NO evidence for using JIVE instead of LIML; LIML has better nite small sample properties. In terms of size, 2SLS is less dispersed than JIVE. The results of DM s paper does not support ndings in Blomquist and Dahlberg (1999) [BD] and Angrist, J., W. Imbens and A. Krueger (1999) [AIK].
6 The case against JIVE Summarizing Finite-sample properties Evaluation (According to each study) UJIVE LIML Comment DM X LIML the best in reducing bias BD?? Hard to nd a winner! AIK X A reduced space of parameters
7 The bias of 2SLS The System of Equations We have the following system of equations (in matricial terms); Y = X β + ε (1) X = Z π + η (2) where X, Z and η are matrices of dimension n L, n k and n L respectively. The number of overidenti ed restricctions can be calculated as r = k L. Also, there are M common elements in X and Z, then M columns of n L matrix η are zero. The endogeneity comes from the following expression E ε i η 0 i Z = σ εη (3)
8 The bias of 2SLS The bias of OLS We have the following assumptions E [ ηi 0j Z ] = 0 and E [ η i ηi 0j Z ] = Σ η. The rank of Σ η is equal to L M. The inconsistency feature of OLS estimator β OLS = X 0 X 1 X 0 Y is shown in the following steps β OLS = (Z π + η) 0 (Z π + η) 1 (Z π + η) 0 Y = η 0 + π 0 Z 0 (Z π + η) 1 (Z π + η) 0 Y
9 The bias of 2SLS The bias of OLS β OLS = η 0 + π 0 Z 0 (Z π + η) 1 η 0 + π 0 Z 0 Y = η 0 + π 0 Z 0 (Z π + η) 1 η 0 + π 0 Z 0 (X β + ε) = η 0 + π 0 Z 0 (Z π + η) 1 η 0 + π 0 Z 0 ((Z π + η) β + ε) Then applying law of iterative expectations ((η E [E [β Z OLS ]j Z ] = E 0 + π 0 Z 0 ) (Z π + η)) 1 (η 0 + π 0 Z 0 ) ((Z π + η) β + ε) Z
10 The bias of 2SLS The bias of OLS β + ((η E [E [β Z OLS ]j Z ] = E 0 + π 0 Z 0 ) (Z π + η)) 1 (η 0 + π 0 Z 0 ) ε Z h = E β + η 0 + π 0 Z 0 (Z π + η) i 1 η 0 ε Z " (η = β π 0 Z 0 # ) (Z π + η) 1 η 0 ε E N N Z In terms of consistency lim N! β OLS = β + π0 Σ Z π + Σ η 1 σεη
11 The bias of 2SLS The bias of OLS lim N! β OLS = β + π0 Σ Z π + Σ η 1 σεη Z Where Σ Z = lim 0 Z N! N, Σ η η = lim 0 η N! N and η0 ε N p! σ εη.
12 The bias of 2SLS The bias of 2SLS The optimal instrumental variable estimation must ful ll the following condition E (Y X β IV ) 0 Θ (Z ) = 0 an analytical solution is available since Y 0 Θ (Z ) X 0 Θ (Z ) 1 Y 0 Θ (Z ) = β 0 IV X 0 Θ (Z ) = β 0 IV or β IV = Θ (Z ) 0 X 1 Θ (Z ) 0 Y Woodridge states that Θ (Z ) = Z π is the optimal instrument in terms of e ciency (instead of only Z).
13 The bias of 2SLS k-class estimator Note that (Z bπ) 0 = X 0 P Z = X 0 Z (Z 0 Z ) 1 Z 0. P Z is the orthogonal projection on to the span of the columns of Z. Following to Davidson and Mackinnon (2007) we must take notice that we can nd a matrix A with the property that AZ = Z will lead us to have another estimator. Particularly, if we set up the choice A = I κ (I P Z ), we have a κ class estimator. Thus, quite generally we consider the estimator β by using Θ (Z ) Θ (Z, κ).
14 The bias of 2SLS The bias of 2SLS because π is unknown (unfeasible estimation) we approach the estimator with a feasible version of the optimal IV estimation bβ 2SLS IV = (Z bπ) 0 X 1 (Z bπ) 0 Y (4) where bπ = (Z 0 Z ) 1 Z 0 X.It is value to take notice that expression (4) is not properly the estimator for 2SLS; [AIK] states that β 2SLS IV has much better small sample properties than β 2SLS in the presence of many instruments (Nagar; 1959).
15 The bias of 2SLS The bias of 2SLS We show the bias of 2SLS estimator in the following lines E [ε i Z i bπ] = E [E [ε i Z i bπ]j Z ] Z h = E he ε i Z i Z 0 Z i i 1 Z 0 X Z Z = E hz i Z 0 Z i 1 Z 0 E [ε i X ] Z Z = E hz i Z 0 Z i 1 Z 0 E [ε i (Z π + η)] Z Z = E hz i Z 0 Z i 1 Z 0 E [ε i Z π + ε i η] Z Z = E hz i Z 0 Z i 1 Z 0 E [ε i η] Z Z = E hz i Z 0 Z i 1 Z 0 Ξ εi η Z Z
16 The bias of 2SLS The bias of 2SLS where Ξ 0 ε i η is a row vector with zeros and just one element σ εη 6= 0 in the i-position. Equivalently, E [ε i Z i bπ] = E hz i Z 0 Z i 1 Z 0 Ξ εi η Z Z h = E Z i Z 0 Z i 1 Z 0 i E [ε i η Z i ] Z h = E Z i Z 0 Z i 1 Z 0 i Z σ 0 εη Z = K N σ εη Thus, for a xed σ εη we have that for small samples E [ε i Z i bπ] increases with the number of instruments. The result is that we have a bias in the 2SLS estimator.
17 Estimators UJIVE 1 UJIVE 1 JIVE removes the dependence of of the constructed instrument Z i bπ on the endogenous regressor for observation i by using the following estimator eπ (i) = Z (i) 0 Z (i) 1 Z (i) 0 X (i) (5) the estimate of the optimal instrument is Z i eπ (i) ; then, because ε i is independent of X j if j 6= i we claim that E [ε i Z i eπ (i)] = 0 this is easily veri able E E ε i Z 0 i eπ (i) Z E = 0 h Z i Z (i) 0 Z (i) i 1 Z (i) 0 E [εi X (i)] Z See Phillips and Hale (1977) for details.
18 Estimators UJIVE 1 UJIVE 1 Thus, bx i,ujive = Z i eπ (i) ; then the estimator of β is bβ UJIVE = 1 X b UJIVE 0 X X b UJIVE 0 Y (UJIVE 1) We require to perform the estimator in (5) by each observation i. [AIK] show a sort of shortcut where h i = Z i (Z 0 Z ) 1 Z 0 i Z i eπ (i) = Z i bπ h i X i 1 h i
19 Estimators UJIVE 2 UJIVE 2 An alternative estimator is Z i eπ (i) = Z i bπ the resulting estimator for β is bβ UJIVE 2 = 1 1 N h i X i 1 X b UJIVE 0 2 X X b UJIVE 0 2Y (UJIVE 2) where bx i,ujive 2 = Z i eπ (i). The projection between UJIVE1 and UJIVE2 are closely similar and both are consistent. The probability of the estimator of β and their rst-order asymptotic distribution are therefore the same as those of β IV and β 2SLS. DM states that these estimators may di er noticeably in any particular sample.
20 Estimators JLS or JIVE JIVE DM consider that an alternative estimator is bβ JIVE = X b JIVE 0 X b 1 JIVE X b JIVE 0 Y (JIVE) where bx i,jive = Z i π (i). DM states that JIVE is biased in the direction of zero, just as OLS estimator when the explanatory variable is measured with error. But, This class of estimator is consistent.
21 Estimators LIML Limited Information Maximum Likelihood We can estimate the parameters in linear regressions with endogenous regressors by using the limited-information-maximum-likelihood estimator. The likelihood is based on normality for the reduced form errors and with covariance matrix, although consistency and asymptotic normality of the estimator do not rely on this assumption. The log likelihood function is L = N i= ln (2π) ln jωj (LIML) 2 (Zi π) 0 0 β Ω 1 Yi (Zi π) 0 β (6) Z i π Z i π Yi X i X i
22 Experiments Experiments DM have the following system of equations (in matricial terms) in order to do the simualtions; Y = ιβ 1 + x β 2 + ε (Structural eq.) x = σ η (Z π + η) (Reduced eq.) where X = [ι x], Z and η are matrices of dimension n 2, n l and n 1 respectively. The number of overidenti ed restricctions can be calculated as r = l 2. The elements of ε and η have variances σ 2 ε and 1 respectively, and correlation ρ. In order to start with the simulations we need to impose values for parameters. For this, an important guide is the size of the ratio kπk 2 to σ 2 η.
23 Experiments The concentration parameter The ratio kπk 2 to σ 2 η is interpreted as the signal-to-noise ratio in the reduced-form equation.
24 Experiments Setting up parameters DM x values of the π j to be equal excepting π 1 = 0. The parameter which does varies is denoted by R 2 = kπk2 kπk 2 +σ 2 η (This is the asymptotic R 2 ) R 2 is monotonically increasing function of the the ratio kπk 2 to σ 2 η. A small value of R 2 implies that the instruments are weak. In the experiments, DM vary the sample size n, the number of overidentifying restrictions (r), the correlation between errors (ρ) and R 2
25 Experiments Parameters set up Montecarlo replications. When R 2 = 0, β 2 is not asymptotically identi ed. Absolute value of ρ matters; the sign just a ects the direction of bias. r varies from 0 to 16. Sample size: 25, 50, 100, 200, 400 and 800.
26 Experiments Performance evaluation Because LIML and JIVE estimators have no moments (see davison and Mackinnon; 2007). DM reports the median bias, this is median bias = β d 0.5 β As measure of dispersion DM reports the nine decile range, this is 9d range = β d 0.95 β d 0.05 Ackberg and Devereux (2006) suggest to consider Trimmed mean bias = 1 n j β j β where β j 2 [β d 0.99 β d 0.01 ].
27 Results Results (I): Median bias evaluation
28 Results Results (II): Median bias evaluation
29 Results Results (III): Median bias evaluation
30 Results Results (IV): Rejection frequencies
31 Results Results (V): Dispersion
32 Conclusions Conclusions 1 AIK and BD give divergent views of JIVE performance. DM s paper re-examinate this issue. 2 DM conclude that in most regions of the parameters space they have studied, JIVE is inferior to LIML regarding to median bias, dispersion and reliability of inference. 3 LIML should be preferred whenever you need to deal with estimators which have no moments. 4 DM points out that, however, montecarlo simulations does no support unambiguoulsy the usage of LIML; when the instruments are weak the dispersion is signi cant in this estimator. 5 Chao and Swanson (2004) state that LIML is not a consistent estimator in a context of heteroskedasticity; but UJIVE is (under some conditions).
33 Two comments Ackerberg and Devereux s comments They disagree with DM conclusion: The LIML estimator should almost always be prefered to the JIVE estimators. Ackerberg and Devereux (2003) show that advantages over LIML are signi cantly reduced when using the "improved" JIVE (IJIVE). They extend the unbiased estimator (UIJIVE). What matters is the results in the space of weak instruments; the resulting advantages of LIML in terms of median bias and dispersion are small in that space. But not much di erent from IJIVE estimators. There are important advantages of JUVE estimators over the LIML estimator; particualrly regarding the robustness of JIVE estimators to heteroskedasticity.(see Chao and Swanson; 2004).
34 Two comments Ackerberg and Devereux s comments About the performance of IJIVE estimators. Particularly, AD shows that in the region where R 2 > 0.2 the IJIVE estimator removes almost all the median bias of the JIVE estimator. But, LIML is better in terms of bias in the space of weak instruments. IJIVE improves on the 9-decile range of JIVE by about 20%; although it is considerably larger that that of LIML. If they consider the trimmed mean statistics, UIJIVE bias.is smaller than that of LIML.
35 Two comments Ackerberg and Devereux s comments They conclude the following about advantages of LIML By using IJIVE or UIJIVE one can either closely match the median bias of LIML or closely match the dispersion and better the trimmed mean bias of LIML. LIML does better in terms of median bias for values of R 2 below 0.2. But, the emprical work is not possible in that situation; mainly because When R 2 is below 0.2 the average rst stage F-statistic is below 3 and the corresponding p-value is above 0.10; one tipically would not be able to reject the hypothesis that the instruments are irrelevant. The variance of all estimators is likely to be large.
36 Two comments Ackerberg and Devereux s comments LIML is not the panacea IJIVE and UIJIVE appear to be very robust estimators. In particular, these estimators are consistent in the case of heteroskedasticity. Chao and Swanson (2004) states that LIML is not a consistent estimator in this context of heteroskedasticity. Chao and Swanson (2004) provide and alternative proof that JIVE estimators are consistent under heteroskedasticity Could "a sort of" LIML estimator become consistent under this context?. Such estimator would probably not have a closed solution and might be less robust to other perturbations (non-normality) than standard LIML estimator.
37 Two comments Blomquist and Dahlberg s comments they do nd di cult to understand categorical rejection of JIVE from DM; JIVE or LIML do not dominate the 2SLS in terms of RSME. In terms of bias, DM s results shows a good perfomance of LIML. In terms of variance 2SLS outperforms both LIML and JIVE estimators. LIML outperforms JIVE for some values of the parameter space, in others spaces we nd the opposite conclusion. The complexity of the DGP matter for a conclusion. AIK, BD and DM should be more nuanced.
38 ... and One reply Davidson and Mackinnon s reply DM agree that there is some space of parameters where UJIVE outperforms LIML. They do simulations and evaluate the perform of UIJIVE s Ackerberg and Devereux (2006); interestingly, UIJIVE tends to be subtantially less dispersed than other JIVE estimators and just when the instruments are weak the this IJIVE is less dispersed than LIML. They propose to look at n 1/2 bβ 2 β 2 = t 0 + n 1/2 t 1 + o p n 1/2 to show the approximate biases for these estimators.
39 ... and One reply Davidson and Mackinnon s reply They states out that altought UIJIVE si constructed to reduce mean bias; it does not do nearly so well as regards median bias. That implies that estimator is highly skewed. DM proposes to look more closely at modi ed LIML estimator proposed by Fuller (1977) for which the moment exist and then see how it performs relative to UIJIVE.
40 Estimation by using STATA STATA command In order to perform the UJIVE estimator there is an available STATA command for that; the syntaxis is as follows jive depvar [varlist1] (varlist2 =varlistiv) [if] [in] [, options] The options are UJIVE1, UJIVE2 (see AIK), JIVE1 JIVE 2 (see BD) and calculation of a robust matrix for dealing with heteroskedasticity. The command jive saves information in e(), the most interesting matrices are: e(b) -the coe cient vector, e(v) -the variance and covariance matrix, e(f1) - rst stage F stat and e(r2_1) - rst stage R 2.
41 References References Angrist, J., W. Imbens and A. Krueger (1999). Jaccknife Instrumental Variables Estimation. Journal of Applied Econometrics 14: Blomquist and Dahlberg (1999). Small sample properties of LIML and Jaccknife IV estimators: Experiments with Weak Instruments. Journal of Applied Econometrics 14: Davidson, R., and J. McKinnon (2004). The case Against JIVE. Journal of Applied Econometrics 21: Davidson, R., and J. McKinnon (2006). Reply to Ackerberg and Devereux and Blomquist and Dhalberg on "The case Against JIVE". Journal of Applied Econometrics 21:
42 References References Blomquist and Dahlberg (2006). The case Against JIVE: A comment. Journal of Applied Econometrics 21: Ackerberg and Deverwux (2006)..Comment on "The case Against JIVE". Journal of Applied Econometrics 21: Davidson, R., and J. McKinnon (2007). Moments of IV and JIVE estimators. The Econometrics Journal Vol 10 Number 3. Stock, J., J. Wright and M. Yogo (2002). A Survey of Weak Instruments and Weak Identi cation in Generalized Method of Moments. Journal of Business and Economic Statistics, Vol 20 Number 4. Hausman, J., W. Newey, T. Woutersen, J. Chao and N. Swanson (2006). Instrumental variable Estimation with Heteroskedasticity and Many Instruments. Working paper.
43 References References Chao, J. and N. Swanson. (2004). Estimation and Testing Using Jackknife IV in heteroskedasticity Regressions With many Weak Instruments. Working paper, Rutgers University. Nagar, A. (1959). The Bias and Moment matrix of the general k-class estimators of the parameters in simultaneous equation. Econometrics, 27, Phillips, G. D. A., and C. Hale. (1977). The bias of instrumental variable estimators of simultaneous equation systems. International Economic Review 18: Fuller, W.A. (1977) Some properties of a modi cation of the Limited Information estimator. Econometrica 45,
44 The Case Against JIVE when Instruments are Weak References Notes References Chao, J. and N. Swanson. (2004). Estimation and Testing Using Jackknife IV in heteroskedasticity Regressions With many Weak Instruments. Working paper, Rutgers University. Nagar, A. (1959). The Bias and Moment matrix of the general k-class estimators of the parameters in simultaneous equation. Econometrics, 27, Phillips, G. D. A., and C. Hale. (1977). The bias of instrumental variable estimators of simultaneous equation systems. International Economic Review 18: Fuller, W.A. (1977) Some properties of a modi cation of the Limited Information estimator. Econometrica 45, Notes
45 Appendix AIK results DGP Median Absolute Error N=100, L=2, M=5000 Estimators 2SLS LIML UJIVE1 UJIVE2 OLS
46 Appendix AIK results DGP Coverage rate 95% conf. Interval N=100, L=2, M=5000 Estimators 2SLS LIML UJIVE1 UJIVE2 OLS
47 The Case Against JIVE when Instruments are Weak Appendix Appendix Notes AIK results Coverage rate 95% conf. Interval N=100, L=2, M=5000 DGP Estimators 2SLS LIML UJIVE1 UJIVE2 OLS Notes The DGP processes for each model are as follows 1. There is a single overidentifying restriction K=3, L=2 and ρ = A large number of instruments relative to the number of regressors; K=21, L=2 and ρ = The model is non-linear and heteroscedatic; K=21, L=2 and ρ = This model sets the true reduced-form coe cients to zero for all instruments in an attempt to ascertain how misleading the estimators might be in this non-identi ed case; K=21, L=2 and ρ = AIK introduces a misspeci cation; one of the instruments has incorrectly been left out of the main regression; K=21, L=2 and ρ = 0.25
48 Appendix BD results Stats MEAN BIAS MEDIAN BIAS RMSE SIZE Results of Simulations ρ = 0.2, M=1000 replications Estimators 2SLS LIML UJIVE USSIV OLS
49 The Case Against JIVE when Instruments are Weak Appendix Notes BD results Stats MEAN BIAS MEDIAN BIAS RMSE SIZE Results of Simulations ρ = 0.2, M=1000 replications Estimators 2SLS LIML UJIVE USSIV OLS Notes 1. The percent bias is de ned as (ˆδ-δ)/δ. 2. The rst and second row in each statistic refers to sample size equal to 500 and 4000 respectively.
50 Appendix BD results Stats MEAN BIAS MEDIAN BIAS RMSE SIZE Results of Simulations ρ = 0.6, M=1000 replications Estimators 2SLS LIML UJIVE USSIV OLS
The Case Against JIVE
The Case Against JIVE Davidson and McKinnon (2004) JAE 21: 827-833 PhD. student Freddy Rojas Cama Econometrics Theory II Rutgers University November 14th, 2011 Literature 1 Literature 2 The case against
More informationSymmetric Jackknife Instrumental Variable Estimation
Symmetric Jackknife Instrumental Variable Estimation Paul A. Bekker Faculty of Economics and Business University of Groningen Federico Crudu University of Sassari and CRENoS April, 2012 Abstract This paper
More informationImproved Jive Estimators for Overidentied Linear Models with and without Heteroskedasticity
Improved Jive Estimators for Overidentied Linear Models with and without Heteroskedasticity Daniel A. Ackerberg UCLA Paul J. Devereux University College Dublin, CEPR and IZA ovember 28, 2006 Abstract This
More information11. Bootstrap Methods
11. Bootstrap Methods c A. Colin Cameron & Pravin K. Trivedi 2006 These transparencies were prepared in 20043. They can be used as an adjunct to Chapter 11 of our subsequent book Microeconometrics: Methods
More informationImproved Jive Estimators for Overidentified Linear Models. with and without Heteroskedasticity
Improved Jive Estimators for Overidentified Linear Models with and without Heteroskedasticity Daniel A. Ackerberg UCLA Paul J. Devereux University College Dublin, CEPR and IZA October 8, 2008 Abstract
More informationInstrumental Variable Estimation with Heteroskedasticity and Many Instruments
Instrumental Variable Estimation with Heteroskedasticity and Many Instruments Jerry A. Hausman Department of Economics M.I.T. Tiemen Woutersen Department of Economics University of Arizona Norman Swanson
More informationLocation Properties of Point Estimators in Linear Instrumental Variables and Related Models
Location Properties of Point Estimators in Linear Instrumental Variables and Related Models Keisuke Hirano Department of Economics University of Arizona hirano@u.arizona.edu Jack R. Porter Department of
More informationFinite Sample Performance of A Minimum Distance Estimator Under Weak Instruments
Finite Sample Performance of A Minimum Distance Estimator Under Weak Instruments Tak Wai Chau February 20, 2014 Abstract This paper investigates the nite sample performance of a minimum distance estimator
More informationJackknife Instrumental Variable Estimation with Heteroskedasticity
Jackknife Instrumental Variable Estimation with Heteroskedasticity Paul A. Bekker Faculty of Economics and Business University of Groningen Federico Crudu Pontificia Universidad Católica de Valparaíso,
More informationTesting Overidentifying Restrictions with Many Instruments and Heteroskedasticity
Testing Overidentifying Restrictions with Many Instruments and Heteroskedasticity John C. Chao, Department of Economics, University of Maryland, chao@econ.umd.edu. Jerry A. Hausman, Department of Economics,
More informationChapter 2. Dynamic panel data models
Chapter 2. Dynamic panel data models School of Economics and Management - University of Geneva Christophe Hurlin, Université of Orléans University of Orléans April 2018 C. Hurlin (University of Orléans)
More informationNotes on Generalized Method of Moments Estimation
Notes on Generalized Method of Moments Estimation c Bronwyn H. Hall March 1996 (revised February 1999) 1. Introduction These notes are a non-technical introduction to the method of estimation popularized
More informationA Robust Test for Weak Instruments in Stata
A Robust Test for Weak Instruments in Stata José Luis Montiel Olea, Carolin Pflueger, and Su Wang 1 First draft: July 2013 This draft: November 2013 Abstract We introduce and describe a Stata routine ivrobust
More informationQED. Queen s Economics Department Working Paper No Moments of IV and JIVE Estimators
QED Queen s Economics Department Working Paper No. 1085 Moments of IV and JIVE Estimators Russell Davidson McGill University James MacKinnon Queen s University Department of Economics Queen s University
More informationInference about Clustering and Parametric. Assumptions in Covariance Matrix Estimation
Inference about Clustering and Parametric Assumptions in Covariance Matrix Estimation Mikko Packalen y Tony Wirjanto z 26 November 2010 Abstract Selecting an estimator for the variance covariance matrix
More informationEconomics 241B Estimation with Instruments
Economics 241B Estimation with Instruments Measurement Error Measurement error is de ned as the error resulting from the measurement of a variable. At some level, every variable is measured with error.
More informationECONOMETRICS FIELD EXAM Michigan State University May 9, 2008
ECONOMETRICS FIELD EXAM Michigan State University May 9, 2008 Instructions: Answer all four (4) questions. Point totals for each question are given in parenthesis; there are 00 points possible. Within
More informationInstrumental Variables. Ethan Kaplan
Instrumental Variables Ethan Kaplan 1 Instrumental Variables: Intro. Bias in OLS: Consider a linear model: Y = X + Suppose that then OLS yields: cov (X; ) = ^ OLS = X 0 X 1 X 0 Y = X 0 X 1 X 0 (X + ) =)
More informationOn GMM Estimation and Inference with Bootstrap Bias-Correction in Linear Panel Data Models
On GMM Estimation and Inference with Bootstrap Bias-Correction in Linear Panel Data Models Takashi Yamagata y Department of Economics and Related Studies, University of York, Heslington, York, UK January
More informationImbens/Wooldridge, Lecture Notes 13, Summer 07 1
Imbens/Wooldridge, Lecture Notes 13, Summer 07 1 What s New in Econometrics NBER, Summer 2007 Lecture 13, Wednesday, Aug 1st, 2.00-3.00pm Weak Instruments and Many Instruments 1. Introduction In recent
More informationHeteroskedasticity-Robust Inference in Finite Samples
Heteroskedasticity-Robust Inference in Finite Samples Jerry Hausman and Christopher Palmer Massachusetts Institute of Technology December 011 Abstract Since the advent of heteroskedasticity-robust standard
More informationBootstrapping Heteroskedasticity Consistent Covariance Matrix Estimator
Bootstrapping Heteroskedasticity Consistent Covariance Matrix Estimator by Emmanuel Flachaire Eurequa, University Paris I Panthéon-Sorbonne December 2001 Abstract Recent results of Cribari-Neto and Zarkos
More informationA Course on Advanced Econometrics
A Course on Advanced Econometrics Yongmiao Hong The Ernest S. Liu Professor of Economics & International Studies Cornell University Course Introduction: Modern economies are full of uncertainties and risk.
More informationPANEL DATA RANDOM AND FIXED EFFECTS MODEL. Professor Menelaos Karanasos. December Panel Data (Institute) PANEL DATA December / 1
PANEL DATA RANDOM AND FIXED EFFECTS MODEL Professor Menelaos Karanasos December 2011 PANEL DATA Notation y it is the value of the dependent variable for cross-section unit i at time t where i = 1,...,
More informationChapter 6: Endogeneity and Instrumental Variables (IV) estimator
Chapter 6: Endogeneity and Instrumental Variables (IV) estimator Advanced Econometrics - HEC Lausanne Christophe Hurlin University of Orléans December 15, 2013 Christophe Hurlin (University of Orléans)
More informationWhat s New in Econometrics. Lecture 13
What s New in Econometrics Lecture 13 Weak Instruments and Many Instruments Guido Imbens NBER Summer Institute, 2007 Outline 1. Introduction 2. Motivation 3. Weak Instruments 4. Many Weak) Instruments
More informationEconometrics II. Lecture 4: Instrumental Variables Part I
Econometrics II Lecture 4: Instrumental Variables Part I Måns Söderbom 12 April 2011 mans.soderbom@economics.gu.se. www.economics.gu.se/soderbom. www.soderbom.net 1. Introduction Recall from lecture 3
More informationEmpirical Methods in Applied Economics
Empirical Methods in Applied Economics Jörn-Ste en Pischke LSE October 2007 1 Instrumental Variables 1.1 Basics A good baseline for thinking about the estimation of causal e ects is often the randomized
More informationThe Hausman Test and Weak Instruments y
The Hausman Test and Weak Instruments y Jinyong Hahn z John C. Ham x Hyungsik Roger Moon { September 7, Abstract We consider the following problem. There is a structural equation of interest that contains
More informationSpecification Test for Instrumental Variables Regression with Many Instruments
Specification Test for Instrumental Variables Regression with Many Instruments Yoonseok Lee and Ryo Okui April 009 Preliminary; comments are welcome Abstract This paper considers specification testing
More informationEconometrics II. Nonstandard Standard Error Issues: A Guide for the. Practitioner
Econometrics II Nonstandard Standard Error Issues: A Guide for the Practitioner Måns Söderbom 10 May 2011 Department of Economics, University of Gothenburg. Email: mans.soderbom@economics.gu.se. Web: www.economics.gu.se/soderbom,
More informationFöreläsning /31
1/31 Föreläsning 10 090420 Chapter 13 Econometric Modeling: Model Speci cation and Diagnostic testing 2/31 Types of speci cation errors Consider the following models: Y i = β 1 + β 2 X i + β 3 X 2 i +
More informationOn the Sensitivity of Return to Schooling Estimates to Estimation Methods, Model Specification, and Influential Outliers If Identification Is Weak
DISCUSSION PAPER SERIES IZA DP No. 3961 On the Sensitivity of Return to Schooling Estimates to Estimation Methods, Model Specification, and Influential Outliers If Identification Is Weak David A. Jaeger
More informationA New Approach to Robust Inference in Cointegration
A New Approach to Robust Inference in Cointegration Sainan Jin Guanghua School of Management, Peking University Peter C. B. Phillips Cowles Foundation, Yale University, University of Auckland & University
More informationThe Exact Distribution of the t-ratio with Robust and Clustered Standard Errors
The Exact Distribution of the t-ratio with Robust and Clustered Standard Errors by Bruce E. Hansen Department of Economics University of Wisconsin October 2018 Bruce Hansen (University of Wisconsin) Exact
More informationRegularized Empirical Likelihood as a Solution to the No Moment Problem: The Linear Case with Many Instruments
Regularized Empirical Likelihood as a Solution to the No Moment Problem: The Linear Case with Many Instruments Pierre Chaussé November 29, 2017 Abstract In this paper, we explore the finite sample properties
More informationEstimator Averaging for Two Stage Least Squares
Estimator Averaging for Two Stage Least Squares Guido Kuersteiner y and Ryo Okui z This version: October 7 Abstract This paper considers model averaging as a way to select instruments for the two stage
More informationEstimation of Time-invariant Effects in Static Panel Data Models
Estimation of Time-invariant Effects in Static Panel Data Models M. Hashem Pesaran University of Southern California, and Trinity College, Cambridge Qiankun Zhou University of Southern California September
More informationGMM-based inference in the AR(1) panel data model for parameter values where local identi cation fails
GMM-based inference in the AR() panel data model for parameter values where local identi cation fails Edith Madsen entre for Applied Microeconometrics (AM) Department of Economics, University of openhagen,
More informationGMM based inference for panel data models
GMM based inference for panel data models Maurice J.G. Bun and Frank Kleibergen y this version: 24 February 2010 JEL-code: C13; C23 Keywords: dynamic panel data model, Generalized Method of Moments, weak
More informationLikelihood Ratio Based Test for the Exogeneity and the Relevance of Instrumental Variables
Likelihood Ratio Based est for the Exogeneity and the Relevance of Instrumental Variables Dukpa Kim y Yoonseok Lee z September [under revision] Abstract his paper develops a test for the exogeneity and
More informationShort T Panels - Review
Short T Panels - Review We have looked at methods for estimating parameters on time-varying explanatory variables consistently in panels with many cross-section observation units but a small number of
More informationSimple Estimators for Semiparametric Multinomial Choice Models
Simple Estimators for Semiparametric Multinomial Choice Models James L. Powell and Paul A. Ruud University of California, Berkeley March 2008 Preliminary and Incomplete Comments Welcome Abstract This paper
More informationChapter 6. Panel Data. Joan Llull. Quantitative Statistical Methods II Barcelona GSE
Chapter 6. Panel Data Joan Llull Quantitative Statistical Methods II Barcelona GSE Introduction Chapter 6. Panel Data 2 Panel data The term panel data refers to data sets with repeated observations over
More informationEconomics 582 Random Effects Estimation
Economics 582 Random Effects Estimation Eric Zivot May 29, 2013 Random Effects Model Hence, the model can be re-written as = x 0 β + + [x ] = 0 (no endogeneity) [ x ] = = + x 0 β + + [x ] = 0 [ x ] = 0
More informationLecture 4: Linear panel models
Lecture 4: Linear panel models Luc Behaghel PSE February 2009 Luc Behaghel (PSE) Lecture 4 February 2009 1 / 47 Introduction Panel = repeated observations of the same individuals (e.g., rms, workers, countries)
More informationLecture Notes on Measurement Error
Steve Pischke Spring 2000 Lecture Notes on Measurement Error These notes summarize a variety of simple results on measurement error which I nd useful. They also provide some references where more complete
More informationLecture 11 Weak IV. Econ 715
Lecture 11 Weak IV Instrument exogeneity and instrument relevance are two crucial requirements in empirical analysis using GMM. It now appears that in many applications of GMM and IV regressions, instruments
More informationSimultaneous Equations and Weak Instruments under Conditionally Heteroscedastic Disturbances
Simultaneous Equations and Weak Instruments under Conditionally Heteroscedastic Disturbances E M. I and G D.A. P Michigan State University Cardiff University This version: July 004. Preliminary version
More informationIntroductory Econometrics
Introductory Econometrics Violation of basic assumptions Heteroskedasticity Barbara Pertold-Gebicka CERGE-EI 16 November 010 OLS assumptions 1. Disturbances are random variables drawn from a normal distribution.
More informationGMM Estimation of SAR Models with. Endogenous Regressors
GMM Estimation of SAR Models with Endogenous Regressors Xiaodong Liu Department of Economics, University of Colorado Boulder E-mail: xiaodongliucoloradoedu Paulo Saraiva Department of Economics, University
More informationChapter 1. GMM: Basic Concepts
Chapter 1. GMM: Basic Concepts Contents 1 Motivating Examples 1 1.1 Instrumental variable estimator....................... 1 1.2 Estimating parameters in monetary policy rules.............. 2 1.3 Estimating
More informationGMM Estimation with Noncausal Instruments
ömmföäflsäafaäsflassflassflas ffffffffffffffffffffffffffffffffffff Discussion Papers GMM Estimation with Noncausal Instruments Markku Lanne University of Helsinki, RUESG and HECER and Pentti Saikkonen
More informationE ciency Gains by Modifying GMM Estimation in Linear Models under Heteroskedasticity
E ciency Gains by Modifying GMM Estimation in Linear Models under Heteroskedasticity Jan F. Kiviet and Qu Feng y Version of 5 October, 2015 z JEL-code: C01, C13, C26. Keywords: e ciency, generalized method
More informationEstimation of a Local-Aggregate Network Model with. Sampled Networks
Estimation of a Local-Aggregate Network Model with Sampled Networks Xiaodong Liu y Department of Economics, University of Colorado, Boulder, CO 80309, USA August, 2012 Abstract This paper considers the
More informationMarkov-Switching Models with Endogenous Explanatory Variables. Chang-Jin Kim 1
Markov-Switching Models with Endogenous Explanatory Variables by Chang-Jin Kim 1 Dept. of Economics, Korea University and Dept. of Economics, University of Washington First draft: August, 2002 This version:
More informationECONOMETRICS II (ECO 2401S) University of Toronto. Department of Economics. Spring 2013 Instructor: Victor Aguirregabiria
ECONOMETRICS II (ECO 2401S) University of Toronto. Department of Economics. Spring 2013 Instructor: Victor Aguirregabiria SOLUTION TO FINAL EXAM Friday, April 12, 2013. From 9:00-12:00 (3 hours) INSTRUCTIONS:
More informationAlmost Unbiased Estimation in Simultaneous Equations Models with Strong and / or Weak Instruments
Almost Unbiased Estimation in Simultaneous Equations Models with Strong and / or Weak Instruments Emma M. Iglesias and Garry D.A. Phillips Michigan State University Cardiff University This version: March
More informationGMM estimation of spatial panels
MRA Munich ersonal ReEc Archive GMM estimation of spatial panels Francesco Moscone and Elisa Tosetti Brunel University 7. April 009 Online at http://mpra.ub.uni-muenchen.de/637/ MRA aper No. 637, posted
More informationDay 2A Instrumental Variables, Two-stage Least Squares and Generalized Method of Moments
Day 2A nstrumental Variables, Two-stage Least Squares and Generalized Method of Moments c A. Colin Cameron Univ. of Calif.- Davis Frontiers in Econometrics Bavarian Graduate Program in Economics. Based
More informationComment on HAC Corrections for Strongly Autocorrelated Time Series by Ulrich K. Müller
Comment on HAC Corrections for Strongly Autocorrelated ime Series by Ulrich K. Müller Yixiao Sun Department of Economics, UC San Diego May 2, 24 On the Nearly-optimal est Müller applies the theory of optimal
More informationWe begin by thinking about population relationships.
Conditional Expectation Function (CEF) We begin by thinking about population relationships. CEF Decomposition Theorem: Given some outcome Y i and some covariates X i there is always a decomposition where
More informationApplied Econometrics (MSc.) Lecture 3 Instrumental Variables
Applied Econometrics (MSc.) Lecture 3 Instrumental Variables Estimation - Theory Department of Economics University of Gothenburg December 4, 2014 1/28 Why IV estimation? So far, in OLS, we assumed independence.
More information1 Motivation for Instrumental Variable (IV) Regression
ECON 370: IV & 2SLS 1 Instrumental Variables Estimation and Two Stage Least Squares Econometric Methods, ECON 370 Let s get back to the thiking in terms of cross sectional (or pooled cross sectional) data
More informationStrength and weakness of instruments in IV and GMM estimation of dynamic panel data models
Strength and weakness of instruments in IV and GMM estimation of dynamic panel data models Jan F. Kiviet (University of Amsterdam & Tinbergen Institute) preliminary version: January 2009 JEL-code: C3;
More informationSIMILAR-ON-THE-BOUNDARY TESTS FOR MOMENT INEQUALITIES EXIST, BUT HAVE POOR POWER. Donald W. K. Andrews. August 2011
SIMILAR-ON-THE-BOUNDARY TESTS FOR MOMENT INEQUALITIES EXIST, BUT HAVE POOR POWER By Donald W. K. Andrews August 2011 COWLES FOUNDATION DISCUSSION PAPER NO. 1815 COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
More informationWhen is it really justifiable to ignore explanatory variable endogeneity in a regression model?
Discussion Paper: 2015/05 When is it really justifiable to ignore explanatory variable endogeneity in a regression model? Jan F. Kiviet www.ase.uva.nl/uva-econometrics Amsterdam School of Economics Roetersstraat
More informationPanel Data. March 2, () Applied Economoetrics: Topic 6 March 2, / 43
Panel Data March 2, 212 () Applied Economoetrics: Topic March 2, 212 1 / 43 Overview Many economic applications involve panel data. Panel data has both cross-sectional and time series aspects. Regression
More informationIV Estimation and its Limitations: Weak Instruments and Weakly Endogeneous Regressors
IV Estimation and its Limitations: Weak Instruments and Weakly Endogeneous Regressors Laura Mayoral, IAE, Barcelona GSE and University of Gothenburg U. of Gothenburg, May 2015 Roadmap Testing for deviations
More informationTests for Cointegration, Cobreaking and Cotrending in a System of Trending Variables
Tests for Cointegration, Cobreaking and Cotrending in a System of Trending Variables Josep Lluís Carrion-i-Silvestre University of Barcelona Dukpa Kim y Korea University May 4, 28 Abstract We consider
More informationFinite-sample quantiles of the Jarque-Bera test
Finite-sample quantiles of the Jarque-Bera test Steve Lawford Department of Economics and Finance, Brunel University First draft: February 2004. Abstract The nite-sample null distribution of the Jarque-Bera
More informationExogeneity tests and weak identification
Cireq, Cirano, Départ. Sc. Economiques Université de Montréal Jean-Marie Dufour Cireq, Cirano, William Dow Professor of Economics Department of Economics Mcgill University June 20, 2008 Main Contributions
More informationJan F. KIVIET and Milan PLEUS
Division of Economics, EGC School of Humanities and Social Sciences Nanyang Technological University 14 Nanyang Drive Singapore 637332 The Performance of Tests on Endogeneity of Subsets of Explanatory
More informationCointegration Tests Using Instrumental Variables Estimation and the Demand for Money in England
Cointegration Tests Using Instrumental Variables Estimation and the Demand for Money in England Kyung So Im Junsoo Lee Walter Enders June 12, 2005 Abstract In this paper, we propose new cointegration tests
More informationEstimating the Fractional Response Model with an Endogenous Count Variable
Estimating the Fractional Response Model with an Endogenous Count Variable Estimating FRM with CEEV Hoa Bao Nguyen Minh Cong Nguyen Michigan State Universtiy American University July 2009 Nguyen and Nguyen
More informationIncreasing the Power of Specification Tests. November 18, 2018
Increasing the Power of Specification Tests T W J A. H U A MIT November 18, 2018 A. This paper shows how to increase the power of Hausman s (1978) specification test as well as the difference test in a
More informationAsymptotic Distributions of Instrumental Variables Statistics with Many Instruments
CHAPTER 6 Asymptotic Distributions of Instrumental Variables Statistics with Many Instruments James H. Stock and Motohiro Yogo ABSTRACT This paper extends Staiger and Stock s (1997) weak instrument asymptotic
More informationInstrumental Variables Estimation in Stata
Christopher F Baum 1 Faculty Micro Resource Center Boston College March 2007 1 Thanks to Austin Nichols for the use of his material on weak instruments and Mark Schaffer for helpful comments. The standard
More informationEconomics 620, Lecture 7: Still More, But Last, on the K-Varable Linear Model
Economics 620, Lecture 7: Still More, But Last, on the K-Varable Linear Model Nicholas M. Kiefer Cornell University Professor N. M. Kiefer (Cornell University) Lecture 7: the K-Varable Linear Model IV
More informationSingle-Equation GMM: Endogeneity Bias
Single-Equation GMM: Lecture for Economics 241B Douglas G. Steigerwald UC Santa Barbara January 2012 Initial Question Initial Question How valuable is investment in college education? economics - measure
More informationSimple Estimators for Monotone Index Models
Simple Estimators for Monotone Index Models Hyungtaik Ahn Dongguk University, Hidehiko Ichimura University College London, James L. Powell University of California, Berkeley (powell@econ.berkeley.edu)
More informationDiscriminating between (in)valid external instruments and (in)valid exclusion restrictions
Discussion Paper: 05/04 Discriminating between (in)valid external instruments and (in)valid exclusion restrictions Jan F. Kiviet www.ase.uva.nl/uva-econometrics Amsterdam School of Economics Roetersstraat
More informationTesting Weak Convergence Based on HAR Covariance Matrix Estimators
Testing Weak Convergence Based on HAR Covariance atrix Estimators Jianning Kong y, Peter C. B. Phillips z, Donggyu Sul x August 4, 207 Abstract The weak convergence tests based on heteroskedasticity autocorrelation
More informationModels, Testing, and Correction of Heteroskedasticity. James L. Powell Department of Economics University of California, Berkeley
Models, Testing, and Correction of Heteroskedasticity James L. Powell Department of Economics University of California, Berkeley Aitken s GLS and Weighted LS The Generalized Classical Regression Model
More informationNonparametric Identi cation and Estimation of Truncated Regression Models with Heteroskedasticity
Nonparametric Identi cation and Estimation of Truncated Regression Models with Heteroskedasticity Songnian Chen a, Xun Lu a, Xianbo Zhou b and Yahong Zhou c a Department of Economics, Hong Kong University
More informationWooldridge, Introductory Econometrics, 4th ed. Chapter 15: Instrumental variables and two stage least squares
Wooldridge, Introductory Econometrics, 4th ed. Chapter 15: Instrumental variables and two stage least squares Many economic models involve endogeneity: that is, a theoretical relationship does not fit
More information1 A Non-technical Introduction to Regression
1 A Non-technical Introduction to Regression Chapters 1 and Chapter 2 of the textbook are reviews of material you should know from your previous study (e.g. in your second year course). They cover, in
More informationA CONDITIONAL-HETEROSKEDASTICITY-ROBUST CONFIDENCE INTERVAL FOR THE AUTOREGRESSIVE PARAMETER. Donald W.K. Andrews and Patrik Guggenberger
A CONDITIONAL-HETEROSKEDASTICITY-ROBUST CONFIDENCE INTERVAL FOR THE AUTOREGRESSIVE PARAMETER By Donald W.K. Andrews and Patrik Guggenberger August 2011 Revised December 2012 COWLES FOUNDATION DISCUSSION
More informationSome Recent Developments in Spatial Panel Data Models
Some Recent Developments in Spatial Panel Data Models Lung-fei Lee Department of Economics Ohio State University l ee@econ.ohio-state.edu Jihai Yu Department of Economics University of Kentucky jihai.yu@uky.edu
More informationEconometrics of Panel Data
Econometrics of Panel Data Jakub Mućk Meeting # 6 Jakub Mućk Econometrics of Panel Data Meeting # 6 1 / 36 Outline 1 The First-Difference (FD) estimator 2 Dynamic panel data models 3 The Anderson and Hsiao
More informationOn the Power of Tests for Regime Switching
On the Power of Tests for Regime Switching joint work with Drew Carter and Ben Hansen Douglas G. Steigerwald UC Santa Barbara May 2015 D. Steigerwald (UCSB) Regime Switching May 2015 1 / 42 Motivating
More informationGMM Estimation and Testing II
GMM Estimation and Testing II Whitney Newey October 2007 Hansen, Heaton, and Yaron (1996): In a Monte Carlo example of consumption CAPM, two-step optimal GMM with with many overidentifying restrictions
More informationThe Estimation of Simultaneous Equation Models under Conditional Heteroscedasticity
The Estimation of Simultaneous Equation Models under Conditional Heteroscedasticity E M. I and G D.A. P University of Alicante Cardiff University This version: April 2004. Preliminary and to be completed
More informationMore efficient tests robust to heteroskedasticity of unknown form
More efficient tests robust to heteroskedasticity of unknown form Emmanuel Flachaire To cite this version: Emmanuel Flachaire. More efficient tests robust to heteroskedasticity of unknown form. Econometric
More informationBootstrap Testing in Econometrics
Presented May 29, 1999 at the CEA Annual Meeting Bootstrap Testing in Econometrics James G MacKinnon Queen s University at Kingston Introduction: Economists routinely compute test statistics of which the
More informationIntroduction: structural econometrics. Jean-Marc Robin
Introduction: structural econometrics Jean-Marc Robin Abstract 1. Descriptive vs structural models 2. Correlation is not causality a. Simultaneity b. Heterogeneity c. Selectivity Descriptive models Consider
More informationx i = 1 yi 2 = 55 with N = 30. Use the above sample information to answer all the following questions. Show explicitly all formulas and calculations.
Exercises for the course of Econometrics Introduction 1. () A researcher is using data for a sample of 30 observations to investigate the relationship between some dependent variable y i and independent
More informationTECHNICAL WORKING PAPER SERIES TWO-SAMPLE INSTRUMENTAL VARIABLES ESTIMATORS. Atsushi Inoue Gary Solon
TECHNICAL WORKING PAPER SERIES TWO-SAMPLE INSTRUMENTAL VARIABLES ESTIMATORS Atsushi Inoue Gary Solon Technical Working Paper 311 http://www.nber.org/papers/t0311 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050
More informationThe Exact Distribution of the t-ratio with Robust and Clustered Standard Errors
The Exact Distribution of the t-ratio with Robust and Clustered Standard Errors by Bruce E. Hansen Department of Economics University of Wisconsin June 2017 Bruce Hansen (University of Wisconsin) Exact
More informationComparing the asymptotic and empirical (un)conditional distributions of OLS and IV in a linear static simultaneous equation
Comparing the asymptotic and empirical (un)conditional distributions of OLS and IV in a linear static simultaneous equation Jan F. Kiviet and Jerzy Niemczyk y January JEL-classi cation: C3, C, C3 Keywords:
More information